MinT - Best Known (101, ∞, s)-Nets in Base 3

Best Known (101, ∞, s)-Nets in Base 3

Digital (101, m, 68)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (101, 67)-sequence over F₃, using
- base reduction for sequences [i] based on digital (17, 67)-sequence over F₉, using
  - s-reduction based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

Digital (101, m, 96)-net over F₃ for arbitrarily large m, using

There is no (101, m, 216)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (101, 1073, 216)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹⁰⁷³, 216, S₃, 5, 972), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 108563 189016 846150 756239 993727 463363 349249 041672 126452 683244 733369 843224 635649 625268 252760 944759 424342 143309 804244 088082 668437 066557 679235 875209 774462 404266 794124 291257 206340 840850 320109 523609 798294 779555 861323 662983 440391 347451 797866 213895 642883 892768 891751 186167 385903 592066 029586 701385 064346 991437 842758 775874 924830 918558 632353 634886 847975 968689 703086 312793 448108 742466 405334 799092 128182 224951 935327 450908 280627 919673 519317 548589 403679 040545 746501 008028 304816 831336 063633 165416 637473 689906 460115 211298 934839 176445 / 973 > 3¹⁰⁷³ [i]